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Let us assume that selling price of the cloth is $100
5% profit on selling price is $5
So cost price = $95
consider it costs $y for Loren to buy the cloth
$95 cost price <----->$5 profit
$y cost price <---->$45.5 profit

y = \(\frac{45.5*95}{5}\) = $864.5

Correct Answer - E


+1 kudos if you like the solution
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Bunuel
Loren bought a roll of cloth and sold it for a 5% profit based on the selling price. If Loren`s profit was $45.5 total on the cloth, how much did it cost her to buy the cloth?

A. $455.
B. $525.5.
C. $675.
D. $810.5.
E. $864.5.


Let x be the cost price of the roll of cloth. Now the cloth is sold at 5% profit i.e.105% of x = 105% * x.
And above value includes the profit of $45.5.
So, 105% * x = x + 45.5
105x = 100x + 4550.
Solving it we get 5x = 910. Now this amount includes profit of 45.5.
Hence 910-45.5 = $864.5.
Solution is E.
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Good, some learning for me. As others explained, there is a difference between profit based on cost and profit based on selling price.
If there was profit based on cost, then if the cost is 100, selling price is 105.

But this question says if spend = 100, then profit is 5% based on 100. This implies cost = 95. Let us set up a ratio
5/95 = 45.5/x. where x represents the cost.
solving this we get x = 19*45.5 = 20*45.5-45.5 = 910-45.5 = 914.5 - 50 = 864.5.
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Bunuel
Loren bought a roll of cloth and sold it for a 5% profit based on the selling price. If Loren`s profit was $45.5 total on the cloth, how much did it cost her to buy the cloth?

A. $455.
B. $525.5.
C. $675.
D. $810.5.
E. $864.5.

Let selling Price be $ 100
So, Profit is $ 5
And Cost price is $ 95

Quote:
Profit based on the selling price..............profit was $45.5 total on the cloth, how much did it cost her to buy the cloth?

When Profit is 5 ; Cost Price is 95
When Profit is 1 ; Cost Price is \(\frac{95}{5}\)
When Profit is 45.5 ; Cost Price is \(\frac{95}{5}\)*45.5 => 864.5

Hence correct answer must be (E)
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Let selling price be x

She made 5% profit on sale.

\(0.05 * X = 45.5\)

X = \(\frac{(45.5 * 100)}{5}\) = 9.1 * 100 = 910

Original cost = \(910 - 45.5 = 900 -40 + 10 - 45.5 = 864.5\)
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Bunuel
Loren bought a roll of cloth and sold it for a 5% profit based on the selling price. If Loren`s profit was $45.5 total on the cloth, how much did it cost her to buy the cloth?

A. $455.
B. $525.5.
C. $675.
D. $810.5.
E. $864.5.

The calculation can be done orally:

5% profit on SP is $45.5
So SP = 20*45.5 = $910

Cost Price = 910 - 45.5 = $864.5
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